\chapter{Introduction}

\section{Background}
There is a type of food called a "Hot Pocket" which has received a notorious reputation for either being too cold or too hot on the inside. In this project, the measurements taken of a Hot Pocket after heating vary and are not always the same depending on many variables. This is the way as it is in science as well. It is usually the case that more measurements than required are taken in order to get a more accurate, but still not quite precise reading. All of the data collected on the Hot Pockets will be plotted and will eventually be fitted approximately to a line by the linear least squares method. 

\section{Overview} 
The problem is that there are varying degrees of temperature for each Hot Pocket for each measurement after so much time. That is, for each segment of time, the Hot Pockets never measured to be the same heat. This could be because of many factors including location of the plate in the microwave, location of the Hot Pocket on the plate or simply because each Hot Pocket was unique(even though they were all the same flavor.  

This equation below is a mathematical representation of what happens when the least squares method is used on a set of data. The method finds the minimum sum of the difference between the data points in order to find an approximate curve. Being familiar with this equation is helpful because if anything goes wrong with using the SciLab function "lsq" then it may be possible to determine why.
\begin{eqnarray}
\min_{\infty}\sum_{i=1}^{m}(y_i-f(t_i,x))^{2}
\end{eqnarray}

Using the below data, create a SciLab file to create two matrices which will be used in the lsq function in order to find a curve which best represents the data. The lsq function will return a matrix X. The values in X will determine the terms of the interpolating polynomial. 

\begin{center}
\begin{tabular}{ c || c c c }
Time(s) & & Temp(C) \\
\hline 
60s  & 80.5  & 71.1 & 76.7 \\ \hline 
70s  & 83.3  & 73.9 & 78.9 \\ \hline
80s  & 88.9  & 80   & 83.9 \\ \hline
90s  & 94.4  & 86.1 & 85.6 \\ \hline
100s & 96.7  & 90   & 82.3 \\ \hline
110s & 97.2  & 92.2 & 96.1 \\ \hline
120s & 100   & 98.9 & 105 \\ \hline
\end{tabular}
\end{center}


